Although our previous constructions are fundamentally based on conformal field theory,
one can still find a connection with massive models.
We will investigate this issue more systematically in a separate paper [1]}.
Here we use again Longo-Witten endomorphisms [2]} to construct weakly
localized massive models. Then we show that some of them are actually strictly local by
examining wedge-splitting. Note that in [3]} wedge-splitting has been proved through
modular nuclearity [4]}. We provide both a direct proof of wedge-splitting and
a simple proof of modular nuclearity of certain models.
Once strict locality is demonstrated, one can apply
the standard scattering theory and check that S-matrix is nontrivial.
As we will see, this construction can be considered as a
generalization of the Federbush model. The Federbush model is an integrable model with S-matrix
independent from rapidity [5]}. Local observables in this model have been found in
[6]} for certain range of coupling constant.
We construct Haag-Kastler nets which have the same S-matrix as those Federbush models
with the coupling constant of arbitrary size.
The model has multiple one-particle spectrum, hence the strict locality has not been treated in
[3]}. We construct another family of wedge-local nets (Borchers triples)
using Longo-Witten endomorphisms [2]}. Although strict locality is open for this latter family,
two constructions look quite similar.
